Whereas devices for measuring the interfacial shear and dilatational rheology are readily available, extensional rheometry at interfaces remains essentially unexplored. However, a setup mimicking a 2D filament stretching rheometer, the Cambridge Interfacial Tensiometer, was proposed for this very purpose [Jones and Middelberg, Chem. Eng. Sci. 57, 1711-1722 (2002)]. In the present work, a framework is presented for analyzing the interfacial flow field in such device for Newtonian interfaces in the presence of Marangoni flows. Based on the dimensionless numbers that govern the interfacial flow field, different dominant flow types can be identified and the sensitivity of the device for measuring the extensional interfacial viscosity is determined. For the flow field to be dominated by extensional deformations, either the Marangoni number or the ratio of dilatational viscosity to shear viscosity should be at least an order of magnitude higher than the Trouton ratio. Using an analysis for Newtonian materials, the contribution to the overall force by the extensional stress can be determined. It should be noted that obtaining these viscosities from the Cambridge Interfacial Tensiometer also requires knowledge of the interfacial shear and dilatational rheology together with the surface pressure isotherm. To test the technique and evaluate the model, experiments on a dipalmitoylphosphatidylcholine monolayer at an air-water interface have been performed and analyzed. (C) 2012 The Society of Rheology. [http://dx.doi.org/10.1122/1.4733717]